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This article proposes a general gH-gradient efficient-direction method and aW-gH-gradient efficient method for the optimization problems withinterval-valued functions. The convergence analysis and the step-wisealgorithms of both the methods are presented. It is observed that theW-gH-gradient efficient method converges linearly for a strongly convexinterval-valued objective function. To develop the proposed methods and tostudy their convergence, the idea of strong convexity and sequential criteriafor gH-continuity of interval-valued function are illustrated. In the sequel, anew definition of gH-differentiability for interval-valued functions is alsoproposed. The new definition of gH-differentiability is described with the helpof a newly defined concept of linear interval-valued function. It is noticedthat the proposed gH-differentiability is superior to the existing ones. For agH-differentiable interval-valued function, the relation of convexity with thegH-gradient of an interval-valued function and an optimality condition of aninterval optimization problem are derived. For the derived optimalitycondition, a notion of efficient direction for interval-valued functions isintroduced. The idea of efficient direction is used to develop the proposedgradient methods. As an application of the proposed methods, the least squareproblem for interval-valued data by W-gH-gradient efficient method is solved.The proposed method for least square problems is illustrated by a polynomialfitting and a logistic curve fitting.

Generalized-Hukuhara-Gradient Efficient-Direction Method to Solve  Optimization Problems with Interval-valued Functions and its Application in  Least Squares Problems